In the process of drilling well, the kinematics of drill string is quite complicated. The drill string not only vibrates in longitudinal, transverse and torsional direction, but also random impacts and contacts well wall. Considering the random load of drill bit and rock, contact impact of drill string and well wall, a model is proposed to simulate the contact-impact of drill string and formation. The results show that: in the condition of this article the first principal stress of the drill string can reach to 130 MPa, for the random impacts, the strength of drill collar will reduced under cyclic loading; contact-impact is the principal source of drill premature failure. In this paper, an explicit integration and nonlinear finite element was adopted to simulate the collision between the drill string and formation, the process of the collision between the drill string and formation can be revealed compressively and delicately. Through an example, we can obtain the foundation for nonlinear dynamic theory of drill string system collision in the actual work condition, and has important theory significance and academic value.